Convex Optimisation for Communication Systems

In this thesis new robust methods for the efficient sharing of the radio spectrum for underlay cognitive radio (CR) systems are developed. These methods provide robustness against uncertainties in the channel state information (CSI) that is available to the cognitive radios. A stochastic approach is taken and the robust spectrum sharing methods are formulated as convex optimisation problems. Three efficient spectrum sharing methods; power control, cooperative beamforming and conventional beamforming are studied in detail.  The CR power control problem is formulated as a sum rate maximisation problem and transformed into a convex optimisation problem. A robust power control method under the assumption of partial CSI is developed and also transformed into a convex optimisation problem. A novel method of detecting and removing infeasible constraints from the power allocation problem is presented that results in considerably improved performance. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations.  The concept of cooperative beamforming for spectrum sharing is applied to an underlay CR relay network. Distributed single antenna relay nodes are utilised to form a virtual antenna array that provides increased gains in capacity through cooperative beamforming. It is shown that the cooperative beamforming problems can be transformed into convex optimisation problems. New robust cooperative beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations.  Conventional beamforming to allow efficient spectrum sharing in an underlay CR system is studied. The beamforming problems are formulated and transformed into convex optimisation problems. New robust beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations.